A mathematical modelling study of epiphyseal cartilage calcification

Recent studies in this laboratory have suggested that proteoglycan may function as a Ca ion-exchanger in the calcification of epiphyseal growth plate cartilage. Specifically, it has been proposed that phosphate liberated from hypertrophic chondrocytes may displace calcium ions bound to the anionic groups of proteoglycans, thereby raising the Ca x PO4 activity product above the threshold for precipitation of hydroxyapatite. In order to determine whether this mechanism is quantitatively feasible, a mathematical model of the interaction between Ca, Na, proteoglycan and phosphate has now been developed. This model is based on a general binding theory, and utilizes previously-determined values for the binding constants of the Ca-proteoglycan interaction, inhibition constants for the effect of Na and phosphate on this interaction, and literature values for the concentrations of proteoglycan, Na and Ca in epiphyseal cartilage. Using this approach, it was predicted that the free Ca concentration in epiphyseal cartilage in the absence of phosphate will be 1.55 mM. At 0.7 mM phosphate, the approximate concentration in non-calcified cartilage matrix, the free Ca concentration will be 2.40 mM, corresponding to a Ca x PO4 product of 1.68 (mM)2. In order to achieve a Ca x PO4 product sufficient for spontaneous precipitation of hydroxyapatite [approximately 4.3 (mM)2], a phosphate concentration of approximately 1.40 mM is required. Therefore, calcification of epiphyseal cartilage matrix by the mechanism described above will require an approximate doubling of the phosphate concentration in the pre-calcifying zones, indicating that the release of a fraction of the intracellular phosphate could trigger the calcification process.